SOLUTION: Glenn cuts half a rectangular lawn, 40 m by 30 m, by mowing strips of equal width around the perimeter. Brad cuts the small rectangle left. How wide a strip does Glenn cut so that

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Glenn cuts half a rectangular lawn, 40 m by 30 m, by mowing strips of equal width around the perimeter. Brad cuts the small rectangle left. How wide a strip does Glenn cut so that       Log On


   

Question 286245: Glenn cuts half a rectangular lawn, 40 m by 30 m, by mowing strips of equal width around the perimeter. Brad cuts the small rectangle left. How wide a strip does Glenn cut so that they share the work equally?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Glenn cuts half a rectangular lawn, 40 m by 30 m, by mowing strips of equal width around the perimeter.
Brad cuts the small rectangle left.
How wide a strip does Glenn cut so that they share the work equally?
:
Find the area of half the lawn
1%2F2*40*30 = 600 sq/m
:
let x = the width of the strip mown by Glenn
:
Area of the remaining rectangle
(40-2x) * (30-2x) = 600
FOIL
1200 - 80x - 60x + 4x^2 = 600
Arrange as a quadratic equation
4x^2 - 140x + 1200 - 600 = 9
:
4x^2 - 140x + 600 = 0
Simplify, divide by 4
x^2 - 35x + 150 = 0
Factor
(x-30)(x-5) = 0
Two solutions
x = 30, not reasonable
x = 5 meters is the width of the strip mown by Glenn
:
:
Check; (40-10)*30-10) = 600